Lesson Plan: Finding the Maximum Point of a Parabola

Grade Level: 11th Grade Subject: Algebra 2

Learning Objective: - Students will be able to find the maximum point of a parabola by using the vertex form of a quadratic equation. - Students will understand the relationship between the coefficients of a quadratic equation and the shape of its graph.

DE Standards: - CC.2.3.11.A.1: Understand the relationship between the zeros of a quadratic function and the x-intercepts of its graph. - CC.2.3.11.A.2: Understand the relationship between the vertex of a parabola and the maximum or minimum value of a quadratic function.

Materials: - Whiteboard or blackboard - Markers or chalk - Graphing calculators (optional) - Handouts with practice problems

Duration: 60 minutes

Procedure:

- Introduction (5 minutes):
- Begin the lesson by asking students if they remember what a parabola is and its general shape.
- Show them a visual representation of a parabola on the board and ask them to describe its shape and any key points they notice.

- Activating Strategies (10 minutes):
- Provide students with a real-life scenario that can be modeled by a parabolic equation (e.g., throwing a ball in the air).
- Ask students to brainstorm and discuss in pairs or small groups how they can find the maximum height the ball reaches using algebraic methods.
- After a few minutes, facilitate a class discussion and have students share their ideas.

- Lesson Explanation (15 minutes):
- Introduce the vertex form of a quadratic equation: y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola.
- Explain that the vertex form allows us to easily identify the coordinates of the vertex, which is the maximum or minimum point of the parabola.
- Discuss the significance of the coefficient “a” in determining the shape of the parabola (positive/negative, narrow/wide).

- Guided Practice (15 minutes):
- Provide students with a few examples of quadratic equations in standard form and guide them through the process of converting them to vertex form.
- Emphasize the steps involved in completing the square to obtain the vertex form.
- Solve each example together as a class, ensuring students understand the process and reasoning behind each step.

- Independent Practice (10 minutes):
- Distribute handouts with practice problems for students to solve individually.
- Circulate the classroom to provide assistance and answer any questions.

- Closure (5 minutes):
- Review the key concepts covered in the lesson, including the vertex form of a quadratic equation and its relationship to the maximum point of a parabola.
- Summarize the steps involved in finding the maximum point using the vertex form.
- Ask students to share any insights or connections they made during the lesson.

Criteria for Success: - Students correctly identify the vertex form of a quadratic equation. - Students accurately find the coordinates of the maximum point of a parabola. - Students demonstrate an understanding of the relationship between the coefficients of a quadratic equation and the shape of its graph.

Activating Strategies: - Real-life scenario: Presenting a relatable scenario involving a parabolic equation helps students connect the concept to practical applications. - Collaborative discussion: Encouraging students to discuss and brainstorm in pairs or small groups promotes active engagement and peer learning.